236 
POPULAR SCIENCE REVIEW. 
Or if I was told to write a piece of music in the hey of B , my 
series would tell me it needed 5 sharps as signature ; the 
notes these 5 sharps are to be placed on are got by taking the 
first 5 notes in the Series VII., and so on in the case of any 
number of sharps. 
Another useful rule may be derived from inspecting the 
order in Series VII. 
It may be seen that, if a certain number of sharps is marked 
as the signature of the piece of music, the key note is the 
next note of the natural scale above the last sharp marked as 
its signature. Thus, music written in 1 sharp, which is F, 
is in the key of Gr ; if in 2 sharps, they are F and C, and the 
key is D, &c. 
XI. With regard to the mode of writing the signatures of 
keys, a useful rule is got by dividing the series of fifths (II.) 
into two columns alternately, thus : — 
0 C 1 a 
2D 3 A 
4 E 5 B 
6 #F 7 UG 
Placing the number of sharps needed by these key notes 
beside them, we have got the odd and even number of sharps 
in separate columns. The notes in these columns are now seen 
to rise above each other in 2 series of natural scale intervals, 
beginning from C and Gr respectively. Now, in each of these 
columns the notes require each 2 sharps more than the one 
before. 
From hence arises this plain rule, if I wish to transpose a 
piece one note higher , I must add 2 sha r rps to the signature, 
in order to put it into the right key for its new pitch. And so 
on for each other note it is raised. 
XII. Again, separating Series VII. into two similar columns, 
we get : — 
F C 
G D 
A E 
B F 
Here we see the sharps in signatures may be written in 
two columns of notes in natural succession, starting from F 
and C as the first two sharps, and putting each fresh sharp 
alternately above these two notes. 
The inspection of any signature of music written *in several 
sharps will show that this is done. Our examination of Series 
VII. shows why it is done. 
XIII. The examination of th e flat keys is to be conducted in 
a similar manner as the sharp keys. 
Taking Series V., in which we got the order of fifths falling 
